Long-Term Fairness with Unknown Dynamics

While machine learning can myopically reinforce social inequalities, it may also be used to dynamically seek equitable outcomes. In this paper, we formalize long-term fairness as an online reinforcement learning problem for a policy affecting human populations. This formulation accommodates dynamical control objectives, such as achieving equitable population states, that cannot be incorporated into static formulations of fairness. We demonstrate that algorithmic solutions to the proposed fairness problem can adapt to unknown dynamics and, by sacrificing short-term incentives, drive the policy-population system towards more desirable equilibria. For the proposed setting, we develop an algorithm that adapts recent work in online learning and prove that this algorithm achieves simultaneous probabilistic bounds on cumulative loss and cumulative violations of fairness. In the classification setting subject to group fairness, we compare our proposed algorithm to several baselines, including the repeated retraining of myopic or distributionally robust classifiers, and to a deep reinforcement learning algorithm that lacks fairness guarantees. Our experiments model human populations according to evolutionary game theory and integrate real-world datasets.